Answer:
38.66 meters.
Explanation:
Let's denote the height of the building as 'h' (to be determined). Given that the tower is 30m high, we can use trigonometry to solve for the height of the building.
From the information provided, we can form a right triangle with the height of the tower as one side, the height of the building as another side, and the distance between the tower and the building as the hypotenuse.
Considering the angle of depression of 30 degrees, we have the following equation:
tan(30°) = h / d
Where 'd' is the distance between the tower and the building. We don't have the exact value of 'd,' but we can use the second angle of depression to find the relationship between 'd' and the height of the tower.
Using the angle of depression of 45 degrees, we have:
tan(45°) = 30 / d
We can rearrange this equation to solve for 'd':
d = 30 / tan(45°)
Now we can substitute this value of 'd' into the first equation:
tan(30°) = h / (30 / tan(45°))
To find the value of 'h,' we can solve this equation:
h = (30 / tan(45°)) * tan(30°)
Using a calculator, we can calculate the value of 'h' to be approximately 38.66 meters.
Therefore, the height of the building is approximately 38.66 meters.